Are surface plasmons fermions or bosons?

Question

When photons are converted into surface plasmon in some artificially designed structure such as metal gratings to provide the additional momentum, is the boson character of photons are preserved or lost?

Answer 1

The surface plasmons are bosons. The bosonic nature of photons is preserved.

Plasmons are hybridizations of photons and excitons. Although electrons are fermions, their particle-hole excitations (excitons) are bosonic. Because to create a exciton, one needs to move an electron from one state to another, which is implemented by a fermion bilinear operator $c_{k+q}^\dagger c_{k}$. So each exciton is created as a pair of fermions which is then bosonic. Since both photons and excitons are bosonic, their hybridizations, i.e. plasmons, are also bosonic.

Answer 2

I don't exactly agree with the previous answer. Specifically, plasmons are a quantum of free-electron oscillation (ie plasma), while polaritons are hybridizations of photons and excitons. Excitons are a bound electron-hole pair (a composite boson), and not directly relevant to the concept of plasma oscillations. My understanding is that excitons are more relevant to gapped semiconductor systems, where the conduction band is mostly empty of electrons, while plasmons are more relevant to metals where you intrinsically have a sea of free electrons that can oscillate as a plasma.

However, plasmons, excitons, and polaritons are all bosons of sorts. On top of that, photons can couple to plasmons and excitons (and optical phonons) giving rise to different flavors of polaritons: plasmon-polaritons, exciton-polaritons, and phonon-polaritons.

Answer 3

My guess is that collective oscillations of electrons (or "plasmons") can be treated classically, and thus are neither bosonic nor fermionic. The plasmon is manifestly a many-electron object, and thus has a that is 1/2 * however many electrons comprise the plasmon. For the fundamental wavelength 2L contained along a dimension of length L, the plasmon is comprised of ~Avogadro's number of electrons.

So many spins added together should yield a continuum of spins, which is classical.

I also would surmise that L is much greater than the thermal de Broglie wavelength, reinforcing the case for their being classical.

Finally, plasmons appear in the Drude (classical) model of solids, which gives reasonable agreement with measurements (such as those in Table 1.5 of Ashcroft and Mermin). Quantum effects would appear as corrections, rather than as order-of-magnitude effects (e.g., as the factor-of-100 error in the thermal and electrical conductivity of electrons [which fortuitously cancel in the Wiedemann-Franz ratio]).

I am reasoning qualitatively and have not done any sort of derivation to justify this reasoning. Please feel free to point out any mistakes in my reasoning.